Slow evolution of Europa’s interior: metamorphic ocean origin, delayed metallic core formation, and limited seafloor volcanism

Europa’s ocean lies atop an interior made of metal and silicates. On the basis of gravity data from the Galileo mission, many argued that Europa’s interior, like Earth, is differentiated into a metallic core and a mantle composed of anhydrous silicates. Some studies further assumed that Europa differentiated while (or soon after) it accreted, also like Earth. However, Europa probably formed at much colder temperatures, meaning that Europa plausibly ended accretion as a mixture containing water-ice and/or hydrated silicates. Here, we use numerical models to describe the thermal evolution of Europa’s interior assuming low initial temperatures (~200 to 300 kelvin). We find that silicate dehydration can produce Europa’s current ocean and icy shell. Rocks below the seafloor may remain cool and hydrated today. Europa’s metallic core, if it exists, may have formed billions of years after accretion. Ultimately, we expect the chemistry of Europa’s ocean to reflect protracted heating of the interior.

inside a body. The NASA Galileo spacecraft encountered Europa 11 times from December 1996 to September 2003, up to six of which were used to model the moon's mass and moment of inertia (4,43).
Without any a priori knowledge of the moon's interior structure, one can start simple and model Europa as a two-layer body: a rock-metal interior and ocean-ice shell. However, two-layer models have resulted in rock-metal interior densities that are higher than the bulk density of the neighboring anhydrous moon, Io (4).
A more complex but plausible scenario involves Europa segregating its rock-metal interior into a metallic core and silicate mantle. Three-layer models of Europa cannot provide unique solutions to layer thicknesses and densities. Instead, one may calculate the range of plausible layer sizes with assumed densities or vice versa. Many three-layer models of Europa assume hydrostatic equilibrium and thus are constrained by an MoI of 0.346 ± 0.005 (4,7,10,11). However, a recent reappraisal of Galileo radio doppler data without the assumption of hydrostatic equilibrium estimated Europa's MoI to be 0.3547 ± 0.0024 (43). This suggests a thinner ocean-ice shell and less dense rock-metal interior.
Here we model Europa as a three-layer body using the updated MoI and compare our results with previous studies in Table S3. As predicted by (43), our estimates for Europa's metallic core radius and ocean-ice shell thicknesses are smaller than that of previous studies assuming hydrostatic equilibrium. Additionally, we attribute our smaller layer sizes to our assumed density ranges: ρocean-ice = 950-1050 kg m -3 , ρmantle = 3000-3660 kg m -3 , and ρcore = 5150-8000 kg m -3 . The ocean-ice shell and metallic core density ranges match that of (4). However, our minimum density for the silicate mantle is consistent with a rock-metal differentiated Europa. The upper bound of our density range exceeds that of bulk Io, which is thought to be anhydrous. However, metallic core formation should extract dense components from the mantle, so our upper bound on ρmantle is conservative.
Energy to warm/melt primordial water-ice Here we elaborate on the endmember scenario where Europa starts out ice-rock undifferentiated ( Figure 1A), which ultimately does not change our results. The energy required to raise the interior from Europa's initial temperature to the melting temperature of water-ice determines the delay time (i.e., the start time in our models). If Europa formed as a bulk mixture of ice, rock, and metal, then some of Europa's primordial ice may exist as a high-pressure polymorph, which can have elevated melting temperatures.
Temperature and pressure conditions throughout Europa's interior allow for liquid water and ice Ih-XIII to be stable ( Figure S9). A previous study (50) provides a phase diagram of liquid water and ice Ih, II, III, V, VI, VII, VIII, and X based on a mathematical treatment of experimental data at 0-2500 K and 0.01-100 GPa which span conditions present in icy satellites. While uncertainty in Europa's initial T-P conditions allow for a wide variety of water-ice phases to be simultaneously stable, ice VI is typically the most abundant water-ice phase and comprises ~50% of Europa's primordial ice mass.
If Europa's primordial water-ice makes up ~10% of the satellite's total mass, the energy required to warm up primordial ice to liquid water phase boundary is roughly 5 × 10 5 J kg -1 , 2.5 × 10 5 J kg -1 , and 7 × 10 3 J kg -1 for initial temperatures of 200 K, 250 K, and 350 K, respectively. The latent heat of melting for Ih to liquid water is 344 kJ kg -1 . We do not have the latent heat of melting for high-pressure ice phases transitioning into liquid water. If we further assume that all of Europa's primordial ice will melt with a latent heat of melting that is like that of ice Ih, then only ~3 × 10 4 J kg -1 is needed to melt such ice which is an order of magnitude less than the latent heat of antigorite dehydration of 377 kJ kg -1 (91). However, the heat needed to warm up primordial water-ice to the liquid water phase transition temperature is comparable to the energy needed to devolatize Europa's hydrated silicates. Therefore, we ignore the heat required to melt primordial ice but consider the energy required to warm such ice to the liquid phase transition temperature. We explore an undifferentiated ice-rock-metal state for Europa's accreted state and subsequent thermal evolution.

Fe-FeS liquidus
The composition of Europa's Fe-rich core dictates the size of the metallic core and the temperatures required to initiate rock-metal differentiation. Since the exact composition of Europa's metallic core is unknown, we approximate the metallic core composition to be an Fe-FeS alloy which is often used in gravity-constrained models of Europa's interior structure (see Interior structure modeling). See Figure S10B for the Fe-FeS liquidus temperatures as a function of temperature, pressure, and radial depth.
We refer to (46) for our interpolation of the Fe-FeS liquidus temperatures at < 10 GPa, which is minimum at the eutectic (i.e., ~28 wt.% S at Europa's central pressure of 3.8 GPa prior to rock-metal differentiation). On the Fe-rich side of the eutectic, an Fe-FeS eutectic core results in the largest core size and the lowest liquidus temperatures (~1263 ± 25 K) (46). On the other hand, the pure Fe liquidus is about 1940 K and results in a small metallic core that forms late. Figure S10a shows the Fe-rich side of the Fe-FeS liquidus at 3.8 GPa using Equation 29 from (46).
Energy from metallic core formation The energy released from metallic core formation, ΔEG, is the difference in gravitational binding energy between its undifferentiated and differentiated states. Gravitational binding energy can be represented as where EG is gravitational binding energy (J), G is the gravitational constant (m 3 kg -1 s -2 ), m is mass enclosed (kg), and r is radial distance (m) as a function of mass. Therefore, the gravitational binding energy of a homogenous sphere is The gravitational energy of a differentiated two-layer sphere is the sum of internal energies due to a sphere and shell (i.e., metallic core and silicate mantle). Here we provide an analytical derivation that we verified numerically. Given that we already have the binding energy for a sphere, we can redefine our integral limits to solve for the energy of a shell.
Combining the energy of the differentiated metallic core and silicate mantle gives us where M is mass of the rock-metal interior; R is the radius of the rock-metal interior (m); rc is the radius of the metallic core, and ρc and ρm are the metallic core and silicate mantle densities, respectively. We find that ΔEG is maximized for the largest expected metallic core of ~50% total radius and 5150 kg m -3 density (4), yielding ~ 3.9 × 10 27 J. Metallic core formation could be a self-sustaining process if the core-forming energy is deposited into the metal, providing up at least double the energy per mass than the latent heat of fusion for pure iron (92). The heat from metallic core formation may further dehydrate the silicate mantle using Eq. 4. Importantly, fS and fL remain constant assuming the thermophysical properties of our hydrous/anhydrous mineral assemblages and the temperature range of silicate dehydration does not change. This process may release a pulse of fluid = (10) given that mpulse does not exceed the mass of remaining hydrated silicates. However, the distribution of core-forming heat is beyond the scope of this study.   (60). Additionally, our model starts to break down when radiogenic and tidal heating are simultaneously high (tacc < 3 Myr and Q T = 1 TW). This suggests that a purely conductive model cannot describe heat transport at Europa for such high heating cases. However, convection, while not implemented in our model, would suppress the warming of the rock-metal interior and further delay metallic core formation, thus strengthening our argument that metallic core formation happens late. All figure labels and symbols are the same as Figure 3 in the main text. Temperature contours past 1950 K are not shown.  Figure 3 in the main text, though the Fe-FeS liquidus sulfur content are now summarized in Figure S10.

Fig. S3. Decreasing the initial abundance of hydrated silicates (X) facilitates the warming of the interior, but metallic core formation tends to start billions of years after accretion.
Without tidal heating, our models suggest that metallic core formation begins no earlier than half a billion years. Silicate melting occurs several hundreds to ~1300 km from the seafloor. From the top to bottom row, the models presented vary only by hydrated mass fraction of accreted silicates: X = 100% (nominal) (A-B), 50% (C-D), and 0% (E). All figure labels and symbols are the same as Figure 3 in the main text, though the Fe-FeS liquidus sulfur content are now summarized in Figure S10. Temperature contours past 1950 K are not shown.  (49). Silicates start melting around 2.5-3 Gyr after accretion and near the center of Europa, which may inhibit volcanism. The nominal model presented in the main text is in the middle row (Tacc = 250 K). All figure labels and symbols are the same as Figure 3 in the main text, though the Fe-FeS liquidus sulfur content are now summarized in Figure S10. Myr (E-F), respectively, and that ice-rock subsequent differentiation results in silicate hydration. The plots start after our model Europa completes ice-rock differentiation. We assume enough ice was present to result in 6.8 wt.% H2O by the start of the simulation shown. All figure labels and symbols are the same as Figure 3 in the main text, though the Fe-FeS liquidus sulfur content are now summarized in Figure S10. The changes in the timing of metallic core formation and ocean thickness are less than the changes that arise from our uncertainty in tacc, X, and QT shown in Figures S3-S5. The top and bottom row show models assuming cpd = 900 J kg -1 K -1 (nominal) (A-B) and 1000 J kg -1 K -1 (C-D), respectively. All figure labels and symbols are the same as Figure 3 in the main text, though the Fe-FeS liquidus sulfur content are now summarized in Figure S10. Europa releases enough fluid to form the ocean-ice shell, metallic core formation starts billions of years after accretion, and the outermost silicates remain hydrated. Silicate melting shifts upward by ~500 km when decreasing kd, but silicate volcanism is still unlikely given melt depth. The changes in the timing of metallic core formation and ocean thickness are less than the changes that arise from our uncertainty in tacc, X, and QT shown in Figures S3-S5. The top and bottom row show models assuming kd = 4.2 W m -1 K -1 (nominal) (A-B) and 3.0 W m -1 K -1 (C-D), respectively. All figure labels and symbols are the same as Figure 3 in the main text, though the Fe-FeS liquidus sulfur content are now summarized in Figure S10. The bottom row assumes that the hydrated mineral assemblage is ρh = 3000 kg m -3 and 9 wt.% water, both of which are consistent with the grain density and water content of CM chondrites (18,94). All other parameters remain the same as the nominal model. All figure labels and symbol are the same as Figure 3 in the main text, though the Fe-FeS liquidus sulfur content are now summarized in Figure S10.     Table S3. Densities and thicknesses of three-layer Europa models. In our work, we use MoI = 0.3547 ± 0.0024 which does not require Europa to behave hydrostatically (43). Previous studies assume that Europa is a hydrostatic body by using MoI = 0.346 ± 0.005. While all models presented are geophysically consistent with Gallileo radio doppler data, not all models are geologically or geochemically plausible as discussed in the respective studies (7,8,10,11,97).
Interior structure models may be supplemented by geochemical thermodynamics and meteorite data (7,8). Additionally, the results presented may explore a limited range of plausible density and layer thicknesses.